Question

a cold water tap can fill a bath in 3 min and a hot water tap in 4 min , while a waste pipe can empty it in 6 min . if all these three are used together , how long will it take to fill the bath.

Answer 1

cold water tap can fill a bath in 3 min

so , in one minute it fills = 1/3 bathtub

hot water tap can fill a bath in 4 min

so in one minute it fills = 1/4 bathtub

waste pipe can empty bathtub in 6 min

so in one minute it empty = 1/6 bathtub


all together makes work in one minute = 1/3 + 1/4 - 1/6

= 4/12 + 3/12 - 2/12

= 5 / 12

so it takes , 12/5 minutes

= 2.4 minutes

i. e. 2 minutes 24 seconds

Answer 2

We have,

work done by a cold water tap in 3 minutes = 1
so, work done by the cold water tap in one minute = 1 / 3

work done by the hot water tap in 4 minutes = 1
so, work done by the hot water tap in one minute = 1/4

work done by the waste pipe in 6 min = 1
so, work done by the waste pipe in 1 min = 1/6

thus, work done in 1 min if all the three pipes work together = 1/3 + 1/4 - 1/6 = 5 / 12.

hence, it will take (12 / 5) 2.4 minutes to fill the tub.